Method for increasing control performance of model predictive control cost functions

ABSTRACT

A method for controlling an actuator system of a motor vehicle includes utilizing a model predictive control (MPC) module with an MPC solver to determine optimal positions of one or more actuators of the actuator system. The method further includes receiving a plurality of actuator system parameters, and triggering the MPC solver to generate one or more control commands from plurality of actuator system parameters. The method further includes applying a cost function to reduce a steady-state tracking error in the one or more control commands from the MPC solver and applying the one or more control commands to alter positions of the one or more actuators, and applying a penalty term to the steady-state predictions of positions of the plurality of actuators to limit a difference between a steady-state prediction of the actuator system and a solution from the MPC solver.

INTRODUCTION

The present disclosure relates motor vehicle systems, and more particularly, to motor vehicle control systems utilizing model predictive control.

Internal combustion engines combust an air and fuel mixture within cylinders to drive pistons, which produces drive torque. Air flow into the engine is regulated via a throttle. More specifically, the throttle adjusts throttle area, which increases or decreases air flow into the engine. As the throttle area increases, the air flow into the engine increases. A fuel control system adjusts the rate that fuel is injected to provide a desired air/fuel mixture to the cylinders and/or to achieve a desired torque output. Increasing the amount of air and fuel provided to the cylinders increases the torque output of the engine. Actuators in a variety of other automotive control systems can similarly be utilized to provide feedback and/or variable control inputs to an actuator system according to the positioning, states, or movements of the actuators in the system.

Traditional motor vehicle control systems, however, do not control the actuator systems upon which they operate as accurately as desired. For example, some response outputs that are used in feedback loops for control variables do not update quickly enough to provide close to real time feedback to allow for accurate commands. Further, traditional motor vehicle control systems do not provide a rapid response to control signals or coordinate positional, state, or movement control among various devices that affect the system output parameters.

Thus, while current control systems achieve their intended purpose, there is a need for a new and improved system and method for control that includes faster response variables and improved control accuracy.

SUMMARY

In one aspect of the present disclosure, a method for controlling an actuator system of a motor vehicle, includes utilizing a model predictive control (MPC) module with an MPC solver to determine optimal positions of one or more actuators of the actuator system. The method further includes receiving a plurality of actuator system parameters, triggering the MPC solver to generate one or more control commands from the plurality of actuator system parameters, and computing a steady-state solution of the actuator system over a prediction horizon. The method further includes generating steady-state predictions of positions of the plurality of actuators of the actuator system based on the actuator system inputs, one or more environmental conditions, and the linearized physics-based model of the actuator system, and applying a cost function to reduce a steady-state tracking error in the one or more control commands from the MPC solver. The method further includes applying the one or more control commands to alter positions of the one or more actuators. Applying a cost function further includes applying a penalty term to the steady-state predictions of positions of the plurality of actuators to reduce a difference between a steady-state prediction of the actuator system and a solution from the MPC solver, wherein the penalty term has the following equation:

$\sum\limits_{i = 1}^{ny}{W_{y,i}\left( {y_{i}^{s} - y_{i}^{ref}} \right)}^{2}$ where y^(s)=CA⁻¹B+y_(n) ^(s), such that y^(s) is a nominal steady-state solution to the actuator system, W_(y,i) is a predetermined calibrated weight, B indicates the effects of one or more control inputs on a state of the system, A expresses effects of the previous state on the current state, and C maps a current state of the actuator system to one or more output positions of one or more actuators in the actuator system.

In another aspect of the present disclosure, triggering the MPC solver further includes capturing a relationship between a steady-state response of the actuator system and one or more control inputs, and calculating a steady-state gain for the actuator system.

In still another aspect of the present disclosure, calculating a steady-state gain for the actuator system further includes mapping states of the one or more actuators to output positions of the one or more actuators, and determining a relationship between a previous state of the one or more actuators and a current state of the one or more actuators. Calculating a steady-state gain further includes determining a relationship between the one or more control inputs and the current state of the one or more actuators.

In still another aspect of the present disclosure, computing a steady-state solution of the actuator system further includes determining a steady-state non-linearized solution of the actuator system based on a nominal input.

In still another aspect of the present disclosure, receiving a plurality of actuator system parameters further includes receiving one or more control inputs to the actuator system, and measuring one or more environmental conditions. Receiving a plurality of actuator system parameters further includes calculating a linearized physics-based model of the actuator system; and determining one or more actuator system inputs to the linearized physics-based model.

In still another aspect of the present disclosure, the method further includes generating one or more physical parameters from the linearized physics-based model.

In still another aspect of the present disclosure, applying a cost function further includes calculating the calibrated weight for each control command over the prediction horizon, wherein the prediction horizon is an infinite horizon.

In another aspect of the present disclosure, triggering the MPC solver further includes capturing a relationship between a steady-state response of the actuator system and a control input, computing a steady-state solution of the actuator system over a prediction horizon, and calculating a steady-state gain for the actuator system.

In still another aspect of the present disclosure, calculating a steady-state gain for the actuator system further includes mapping states of the one or more actuators to output positions of the one or more actuators and determining a relationship between a previous state of the one or more actuators and a current state of the one or more actuators. Additionally, calculating a steady-state gain includes determining a relationship between the control input and the current state of the one or more actuators.

In still another aspect of the present disclosure, computing a steady-state solution of the actuator system further includes determining a steady-state non-linearized solution of the actuator system based on a nominal input.

In still another aspect of the present disclosure, receiving a plurality of actuator system parameters further includes receiving one or more control inputs to the actuator system, measuring one or more environmental conditions, and calculating a linearized physics-based model of the actuator system. Receiving a plurality of actuator system parameters further includes determining one or more actuator system inputs to the linearized physics-based model.

In still another aspect of the present disclosure, the method for controlling an actuator system of a motor vehicle includes generating steady-state predictions of the positions of the plurality of actuators of the actuator system based on the actuator system inputs, one or more environmental conditions, and the linearized physics-based model of the actuator system. The method further includes generating one or more physical parameters from the linearized physics-based model.

In still another aspect of the present disclosure, applying a cost function further includes applying a calibrated weight to the steady-state predictions of positions of the plurality of actuators to limit a difference between the steady-state predictions and a solution from the MPC solver, and wherein the calibrated weight is calculated for each control command over the prediction horizon.

In still another aspect of the present disclosure, applying the one or more control commands to alter positions of the one or more actuators further includes taking a measurement of the actuator system once the one or more control commands have been applied to the one or more actuators, and applying the measurement of the actuator system to the linearized physics-based model.

In still another aspect of the present disclosure, applying the measurement further includes applying the measurement of the actuator system as a previous control input to the linearized physics-based model of the actuator system.

In still another aspect of the present disclosure, the actuator system comprises one or more of an air per cylinder (APC) system; a fuel system; a state of charge system; a heating, ventilation, and air conditioning system; and an advanced driver assistance system (ADAS).

In still another aspect of the present disclosure, a system that controls an actuator system of a motor vehicle includes one or more of an air per cylinder (APC) system; a fuel system; a state of charge system; a heating, ventilation, and air conditioning system; and an advanced driver assistance system (ADAS). The system further includes one or more actuators, and a model predictive control (MPC) module with an MPC solver that determines optimal positions of the one or more actuators of the actuator system. The MPC module has a controller, a memory, and an input/output interface, the memory storing program code portions, and the controller configured to execute the program code portions. The program code portions include: a program code portion that receives a plurality of actuator system parameters; a program code portion that triggers the MPC solver to generate one or more control commands from plurality of actuator system parameters; a program code portion that computes a steady-state solution of the actuator system over a prediction horizon; and a program code portion that generates steady-state predictions of positions of the plurality of actuators of the actuator system based on the actuator system inputs, one or more environmental conditions, and the linearized physics-based model of the actuator system. The program code portions further include: a program code portion that applies a cost function to reduce a steady-state tracking error in the one or more control commands from the MPC solver; a program code portion that applies the one or more control commands via the input/output interface to alter positions of the one or more actuators; and a program code portion that applies a penalty term to the steady-state predictions of positions of the plurality of actuators to limit a difference between a steady-state prediction of the actuator system and a solution from the MPC solver. The penalty term has the following equation:

$\sum\limits_{i = 1}^{ny}{W_{y,i}\left( {y_{i}^{s} - y_{i}^{ref}} \right)}^{2}$ where y^(s)=CA⁻¹B+y_(n) ^(s), such that y^(s) is a nominal steady-state solution to the actuator system, W_(y,i) is a predetermined calibrated weight. B indicates the effects of one or more control inputs on a state of the system. A expresses effects of the previous state on the current state, and C maps a current state of the actuator system to one or more output positions of one or more actuators in the actuator system.

In still another aspect of the present disclosure the program code portion that triggers the MPC solver further includes a program code portion that captures a relationship between a steady-state response of the actuator system and one or more control inputs; and a program code portion that calculates a steady-state gain for the actuator system.

In still another aspect of the present disclosure the program code portion that calculates a steady-state gain for the actuator system further includes a program code portion that maps states of the one or more actuators to output positions of the one or more actuators, and a program code portion that determines a relationship between a previous state of the one or more actuators and a current state of the one or more actuators. The program code portion that calculates a steady-state gain further includes a program code portion that determines a relationship between the one or more control inputs and the current state of the one or more actuators.

In still another aspect of the present disclosure the program code portion that computes a steady-state solution of the actuator system further includes a program code portion that determines a steady-state non-linearized solution of the actuator system based on a nominal input.

In still another aspect of the present disclosure the program code that receives a plurality of actuator system parameters further includes a program code portion that receives one or more control inputs to the actuator system, and a program code portion that measures one or more environmental conditions. The program code portion that receives a plurality of actuator system parameters further includes a program code portion that calculates a linearized physics-based model of the actuator system, and a program code portion that determines one or more actuator system inputs to the linearized physics-based model.

In still another aspect of the present disclosure the system further includes a program code portion that generates one or more physical parameters from the linearized physics-based model.

In still another aspect of the present disclosure the program code portion that applies a cost function further includes a program code portion that calculates the calibrated weight for each control command over the prediction horizon, wherein the prediction horizon is an infinite horizon.

In still another aspect of the present disclosure the program code portion that applies the one or more control commands to alter positions of the one or more actuators further includes a program code portion that takes a measurement of the actuator system once the one or more control commands have been applied to the one or more actuators. The program code portion that applies the one or more control commands further includes a program code portion that applies the measurement of the actuator system to the linearized physics-based model.

In still another aspect of the present disclosure the program code portion that applies the measurement further includes a program code portion that applies the measurement of the actuator system as a previous control input to the linearized physics-based model of the actuator system.

In still another aspect of the present disclosure, a method for controlling an actuator system of a motor vehicle includes utilizing a model predictive control (MPC) module with an MPC solver to determine optimal positions of one or more actuators of the actuator system. The method further includes receiving a plurality of actuator system parameters including: receiving one or more control inputs to the actuator system, measuring one or more environmental conditions, calculating a linearized physics-based model of the actuator system, and determining one or more actuator system inputs to the linearized physics-based model. The method further includes triggering the MPC solver to generate one or more control commands from plurality of actuator system parameters by: capturing a relationship between a steady-state response of the actuator system and the one or more control inputs, and computing a steady-state non-linearized solution of the actuator system over a prediction horizon based on a nominal input. The method further includes calculating a steady-state gain for the actuator system by: mapping states of the one or more actuators to output positions of the one or more actuators, determining a relationship between a previous state of the one or more actuators and a current state of the one or more actuators, and determining a relationship between the one or more control inputs and the current state of the one or more actuators. The method further includes generating a steady-state prediction of the positions of the plurality of actuators of the actuator system based on the actuator system inputs, one or more environmental conditions, and the linearized physics-based model of the actuator system, and generating one or more physical parameters from the linearized physics-based model. The method further includes applying a cost function to reduce a steady-state tracking error in the one or more control commands from the MPC solver. The cost function is calculated by applying a calibrated weight to the steady-state prediction to limit a difference between the steady-state prediction and a solution from the MPC solver; and wherein the calibrated weight is calculated for each control command over the prediction horizon. The method further includes applying the one or more control commands to alter positions of the one or more actuators, including taking a measurement of the actuator system once the one or more control commands have been applied to the one or more actuators. The method further includes applying the measurement of the actuator system to the linearized physics-based model by applying the measurement of the actuator system as a previous control input to the linearized physics-based model of the actuator system. The method further includes applying a penalty term to the steady-state predictions of positions of the plurality of actuators to limit a difference between a steady-state prediction of the actuator system and a solution from the MPC solver. The penalty term has the following equation:

$\sum\limits_{i = 1}^{ny}{W_{y,i}\left( {y_{i}^{s} - y_{i}^{ref}} \right)}^{2}$ where y^(s)=CA⁻¹B+y_(n) ^(s), such that y^(s) is a nominal steady-state solution to the actuator system, W_(y,i) is a predetermined calibrated weight. B indicates the effects of one or more control inputs on a state of the system. A expresses effects of the previous state on the current state. C maps a current state of the actuator system to one or more output positions of one or more actuators in the actuator system.

Further objects, aspects and advantages of the present invention will become apparent by reference to the following description and appended drawings wherein like reference numbers refer to the same component, element or feature.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings described herein are for illustration purposes only and are not intended to limit the scope of the present disclosure in any way.

The present disclosure will become more fully understood from the detailed description and the accompanying drawings, wherein:

FIG. 1 is a functional block diagram of an example engine system according to an aspect of the present disclosure;

FIG. 2 is a functional block diagram of an example engine control system according to an aspect of the present disclosure;

FIG. 3 is a functional block diagram of an example engine system according to an aspect of the present disclosure;

FIG. 4 is a flowchart depicting a method of controlling an actuator using model predictive control according to an aspect of the present disclosure;

FIG. 5 is a flowchart depicting an example method of controlling a throttle valve, intake and exhaust valve actuation, and a wastegate of a turbo charger using model predictive control according to an aspect of the present disclosure; and

FIG. 6 is a schematic example of a method of controlling an actuator system using model predictive control with a cost function according to an aspect of the present disclosure.

DETAILED DESCRIPTION

The following description is merely exemplary in nature and is not intended to limit the present disclosure, application, or uses.

As is described in U.S. Pat. Nos. 9,599,053 and 9,605,615, hereby incorporated by reference in their entirety, an engine control module (ECM) controls torque output of an engine. More specifically, the ECM controls actuators of the engine based on target values, respectively, determined based on a requested amount of torque. For example, the ECM controls intake and exhaust camshaft phasing based on target intake and exhaust phaser angles, a throttle valve based on a target throttle opening, an exhaust gas recirculation (EGR) valve based on a target EGR opening, and a wastegate of a turbocharger based on a target wastegate duty cycle.

The ECM could determine the target values individually using multiple single input single output (SISO) controllers, such as proportional integral derivative (PID) controllers. However, when multiple SISO controllers are used, the target values may be set to maintain system stability at the expense of possible fuel consumption decreases. Additionally, calibration and design of the individual SISO controllers may be costly and time consuming.

The ECM of the present disclosure generates the target values using model predictive control (MPC). More specifically, the ECM determines optimum target values by iteratively solving a constrained quadratic optimization problem each control loop. The ECM of the present disclosure solves the optimization problem in a computationally efficient manner.

Referring now to FIG. 1, a functional block diagram of an example engine system 100 is presented. The engine system 100 includes an engine 102 that combusts an air/fuel mixture to produce drive torque for a vehicle based on driver input from a driver input module 104. The engine 102 may be a gasoline spark ignition internal combustion engine.

Air is drawn into an intake manifold 110 through a throttle valve 112. For example only, the throttle valve 112 may include a butterfly valve having a rotatable blade. An engine control module (ECM) 114 controls a throttle actuator module 116, which regulates opening of the throttle valve 112 to control the amount of air drawn into the intake manifold 110.

Air from the intake manifold 110 is drawn into cylinders of the engine 102. While the engine 102 may include multiple cylinders, for illustration purposes a single representative cylinder 118 is shown. For example only, the engine 102 may include 2, 3, 4, 5, 6, 8, 10, and/or 12 cylinders. The ECM 114 may instruct a cylinder actuator module 120 to selectively deactivate some of the cylinders, which may improve fuel economy under certain engine operating conditions.

The engine 102 may operate using a four-stroke cycle. The four strokes, described below, may be referred to as the intake stroke, the compression stroke, the combustion stroke, and the exhaust stroke. During each revolution of a crankshaft (not shown), two of the four strokes occur within the cylinder 118. Therefore, two crankshaft revolutions are necessary for the cylinder 118 to experience all four of the strokes.

During the intake stroke, air from the intake manifold 110 is drawn into the cylinder 118 through an intake valve 122. The ECM 114 controls a fuel actuator module 124, which regulates fuel injection to achieve a target air/fuel ratio. Fuel may be injected into the intake manifold 110 at a central location or at multiple locations, such as near the intake valve 122 of each of the cylinders. In various implementations (not shown), fuel may be injected directly into the cylinders or into mixing chambers associated with the cylinders. The fuel actuator module 124 may halt injection of fuel to cylinders that are deactivated.

The injected fuel mixes with air and creates an air/fuel mixture in the cylinder 118. During the compression stroke, a piston (not shown) within the cylinder 118 compresses the air/fuel mixture. A spark actuator module 126 energizes a spark plug 128 in the cylinder 118 based on a signal from the ECM 114, which ignites the air/fuel mixture. The timing of the spark may be specified relative to the time when the piston is at its topmost position, referred to as top dead center (TDC).

The spark actuator module 126 may be controlled by a timing signal specifying how far before or after TDC to generate the spark. Because piston position is directly related to crankshaft rotation, operation of the spark actuator module 126 may be synchronized with crankshaft angle. Generating spark may be referred to as a firing event. The spark actuator module 126 may have the ability to vary the timing of the spark for each firing event. The spark actuator module 126 may vary the spark timing for a next firing event when the spark timing is changed between a last firing event and the next firing event. The spark actuator module 126 may halt provision of spark to deactivated cylinders.

During the combustion stroke, the combustion of the air/fuel mixture drives the piston away from TDC, thereby driving the crankshaft. The combustion stroke may be defined as the time between the piston reaching TDC and the time at which the piston reaches bottom dead center (BDC). During the exhaust stroke, the piston begins moving away from BDC and expels the byproducts of combustion through an exhaust valve 130. The byproducts of combustion are exhausted from the vehicle via an exhaust system 134.

The intake valve 122 may be controlled by an intake camshaft 140, while the exhaust valve 130 may be controlled by an exhaust camshaft 142. In various implementations, multiple intake camshafts (including the intake camshaft 140) may control multiple intake valves (including the intake valve 122) for the cylinder 118 and/or may control the intake valves (including the intake valve 122) of multiple banks of cylinders (including the cylinder 118). Similarly, multiple exhaust camshafts (including the exhaust camshaft 142) may control multiple exhaust valves for the cylinder 118 and/or may control exhaust valves (including the exhaust valve 130) for multiple banks of cylinders (including the cylinder 118). In various other implementations, the intake valve 122 and/or the exhaust valve 130 may be controlled by devices other than camshafts, such as camless valve actuators. The cylinder actuator module 120 may deactivate the cylinder 118 by disabling opening of the intake valve 122 and/or the exhaust valve 130.

The time when the intake valve 122 is opened may be varied with respect to piston TDC by an intake cam phaser 148. The time when the exhaust valve 130 is opened may be varied with respect to piston TDC by an exhaust cam phaser 150. A phaser actuator module 158 may control the intake cam phaser 148 and the exhaust cam phaser 150 based on signals from the ECM 114. When implemented, variable valve lift (not shown) may also be controlled by the phaser actuator module 158.

The engine system 100 may include a turbocharger that includes a hot turbine 160-1 that is powered by hot exhaust gases flowing through the exhaust system 134. The turbocharger also includes a cold air compressor 160-2 that is driven by the turbine 160-1. The compressor 160-2 compresses air leading into the throttle valve 112. In various implementations, a supercharger (not shown), driven by the crankshaft, may compress air from the throttle valve 112 and deliver the compressed air to the intake manifold 110.

A wastegate 162 may allow exhaust to bypass the turbine 160-1, thereby reducing the boost (the amount of intake air compression) provided by the turbocharger. A boost actuator module 164 may control the boost of the turbocharger by controlling opening of the wastegate 162. In various implementations, two or more turbochargers may be implemented and may be controlled by the boost actuator module 164.

An air cooler (not shown) may transfer heat from the compressed air charge to a cooling medium, such as engine coolant or air. An air cooler that cools the compressed air charge using engine coolant may be referred to as an intercooler. An air cooler that cools the compressed air charge using air may be referred to as a charge air cooler. The compressed air charge may receive heat, for example, via compression and/or from components of the exhaust system 134. Although shown separated for purposes of illustration, the turbine 160-1 and the compressor 160-2 may be attached to each other, placing intake air in close proximity to hot exhaust.

The engine system 100 may include an exhaust gas recirculation (EGR) valve 170, which selectively redirects exhaust gas back to the intake manifold 110. The EGR valve 170 may be located upstream of the turbocharger's turbine 160-1. The EGR valve 170 may be controlled by an EGR actuator module 172 based on signals from the ECM 114.

A position of the crankshaft may be measured using a crankshaft position sensor 180. A rotational speed of the crankshaft (an engine speed) may be determined based on the crankshaft position. A temperature of the engine coolant may be measured using an engine coolant temperature (ECT) sensor 182. The ECT sensor 182 may be located within the engine 102 or at other locations where the coolant is circulated, such as a radiator (not shown).

A pressure within the intake manifold 110 may be measured using a manifold absolute pressure (MAP) sensor 184. In various implementations, engine vacuum, which is the difference between ambient air pressure and the pressure within the intake manifold 110, may be measured. A mass flow rate of air flowing into the intake manifold 110 may be measured using a mass air flow (MAF) sensor 186. In various implementations, the MAF sensor 186 may be located in a housing that also includes the throttle valve 112.

The throttle actuator module 116 may monitor the position of the throttle valve 112 using one or more throttle position sensors (TPS) 190. An ambient temperature of air being drawn into the engine 102 may be measured using an intake air temperature (IAT) sensor 192. The engine system 100 may also include one or more other sensors 193, such as an ambient humidity sensor, one or more knock sensors, a compressor outlet pressure sensor and/or a throttle inlet pressure sensor, a wastegate position sensor, an EGR position sensor, and/or one or more other suitable sensors. The ECM 114 may use signals from the sensors to make control decisions for the engine system 100.

The ECM 114 may communicate with a transmission control module 194 to coordinate shifting gears in a transmission (not shown). For example, the ECM 114 may reduce engine torque during a gear shift. The ECM 114 may communicate with a hybrid control module 196 to coordinate operation of the engine 102 and an electric motor 198.

The electric motor 198 may also function as a generator, and may be used to produce electrical energy for use by vehicle electrical systems and/or for storage in a battery. In various implementations, various functions of the ECM 114, the transmission control module 194, and the hybrid control module 196 may be integrated into one or more modules.

Each system that varies an engine parameter may be referred to as an engine actuator. For example, the throttle actuator module 116 may adjust opening of the throttle valve 112 to achieve a target throttle opening area. The spark actuator module 126 controls the spark plugs to achieve a target spark timing relative to piston TDC. The fuel actuator module 124 controls the fuel injectors to achieve target fueling parameters. The phaser actuator module 158 may control the intake and exhaust cam phasers 148 and 150 to achieve target intake and exhaust cam phaser angles, respectively. The EGR actuator module 172 may control the EGR valve 170 to achieve a target EGR opening area. The boost actuator module 164 controls the wastegate 162 to achieve a target wastegate opening area. The cylinder actuator module 120 controls cylinder deactivation to achieve a target number of activated or deactivated cylinders.

The ECM 114 generates the target values for the engine actuators to cause the engine 102 to generate a target engine output torque. The ECM 114 generates the target values for the engine actuators using model predictive control, as discussed further below.

Referring now to FIG. 2, a functional block diagram of an example engine control system is presented. An example implementation of the ECM 114 includes a driver torque module 202, an axle torque arbitration module 204, and a propulsion torque arbitration module 206. The ECM 114 may include a hybrid optimization module 208. The ECM 114 also includes a reserves/loads module 220, a torque requesting module 224, an air control module 228, a spark control module 232, a cylinder control module 236, and a fuel control module 240.

The driver torque module 202 may determine a driver torque request 254 based on a driver input 255 from the driver input module 104. The driver input 255 may be based on, for example, a position of an accelerator pedal and a position of a brake pedal. The driver input 255 may also be based on cruise control, which may be an adaptive cruise control system that varies vehicle speed to maintain a predetermined following distance. The driver torque module 202 may store one or more mappings of accelerator pedal position to target torque and may determine the driver torque request 254 based on a selected one of the mappings.

An axle torque arbitration module 204 arbitrates between the driver torque request 254 and other axle torque requests 256. Axle torque (torque at the wheels) may be produced by various sources including an engine and/or an electric motor. For example, the axle torque requests 256 may include a torque reduction requested by a traction control system when positive wheel slip is detected. Positive wheel slip occurs when axle torque overcomes friction between the wheels and the road surface, and the wheels begin to slip against the road surface. The axle torque requests 256 may also include a torque increase request to counteract negative wheel slip, where a tire of the vehicle slips in the other direction with respect to the road surface because the axle torque is negative.

The axle torque requests 256 may also include brake management requests and vehicle over-speed torque requests. Brake management requests may reduce axle torque to ensure that the axle torque does not exceed the ability of the brakes to hold the vehicle when the vehicle is stopped. Vehicle over-speed torque requests may reduce the axle torque to prevent the vehicle from exceeding a predetermined speed. The axle torque requests 256 may also be generated by vehicle stability control systems.

The axle torque arbitration module 204 outputs a predicted torque request 257 and an immediate torque request 258 based on the results of arbitrating between the received driver and axle torque requests 254 and 256. As described below, the predicted and immediate torque requests 257 and 258 from the axle torque arbitration module 204 may selectively be adjusted by other modules of the ECM 114 before being used to control the engine actuators.

In general terms, the immediate torque request 258 may be an amount of currently desired axle torque, while the predicted torque request 257 may be an amount of axle torque that may be needed on short notice. The ECM 114 controls the engine system 100 to produce an axle torque equal to the immediate torque request 258. However, different combinations of target values may result in the same axle torque. The ECM 114 may therefore adjust the target values to enable a faster transition to the predicted torque request 257, while still maintaining the axle torque at the immediate torque request 258.

In various implementations, the predicted torque request 257 may be set based on the driver torque request 254. The immediate torque request 258 may be set to less than the predicted torque request 257 under some circumstances, such as when the driver torque request 254 is causing wheel slip on an icy surface. In such a case, a traction control system (not shown) may request a reduction via the immediate torque request 258, and the ECM 114 reduces the engine torque output to the immediate torque request 258. However, the ECM 114 performs the reduction so the engine system 100 can quickly resume producing the predicted torque request 257 once the wheel slip stops.

In general terms, the difference between the immediate torque request 258 and the (generally higher) predicted torque request 257 can be referred to as a torque reserve. The torque reserve may represent the amount of additional torque (above the immediate torque request 258) that the engine system 100 can begin to produce with minimal delay. Fast engine actuators are used to increase or decrease current axle torque with minimal delay. Fast engine actuators are defined in contrast with slow engine actuators.

In general terms, fast engine actuators can change the axle torque more quickly than slow engine actuators. Slow actuators may respond more slowly to changes in their respective target values than fast actuators do. For example, a slow actuator may include mechanical components that require time to move from one position to another in response to a change in target value. A slow actuator may also be characterized by the amount of time it takes for the axle torque to begin to change once the slow actuator begins to implement the changed target value. Generally, this amount of time will be longer for slow actuators than for fast actuators. In addition, even after beginning to change, the axle torque may take longer to fully respond to a change in a slow actuator.

For example only, the spark actuator module 126 may be a fast actuator. Spark-ignition engines may combust fuels including, for example, gasoline and ethanol, by applying a spark. By way of contrast, the throttle actuator module 116 may be a slow actuator.

For example, as described above, the spark actuator module 126 can vary the spark timing for a next firing event when the spark timing is changed between a last firing event and the next firing event. By way of contrast, changes in throttle opening take longer to affect engine output torque. The throttle actuator module 116 changes the throttle opening by adjusting the angle of the blade of the throttle valve 112. Therefore, when the target value for opening of the throttle valve 112 is changed, there is a mechanical delay as the throttle valve 112 moves from its previous position to a new position in response to the change. In addition, air flow changes based on the throttle opening are subject to air transport delays in the intake manifold 110. Further, increased air flow in the intake manifold 110 is not realized as an increase in engine output torque until the cylinder 118 receives additional air in the next intake stroke, compresses the additional air, and commences the combustion stroke.

Using these actuators as an example, a torque reserve can be created by setting the throttle opening to a value that would allow the engine 102 to produce the predicted torque request 257. Meanwhile, the spark timing can be set based on the immediate torque request 258, which is less than the predicted torque request 257. Although the throttle opening generates enough air flow for the engine 102 to produce the predicted torque request 257, the spark timing is retarded (which reduces torque) based on the immediate torque request 258. The engine output torque will therefore be equal to the immediate torque request 258.

When additional torque is needed, the spark timing can be set based on the predicted torque request 257 or a torque between the predicted and immediate torque requests 257 and 258. By the following firing event, the spark actuator module 126 may return the spark timing to an optimum value, which allows the engine 102 to produce the full engine output torque achievable with the air flow already present. The engine output torque may therefore be quickly increased to the predicted torque request 257 without experiencing delays from changing the throttle opening.

The axle torque arbitration module 204 may output the predicted torque request 257 and the immediate torque request 258 to a propulsion torque arbitration module 206. In various implementations, the axle torque arbitration module 204 may output the predicted and immediate torque requests 257 and 258 to the hybrid optimization module 208.

The hybrid optimization module 208 may determine how much torque should be produced by the engine 102 and how much torque should be produced by the electric motor 198. The hybrid optimization module 208 then outputs modified predicted and immediate torque requests 259 and 260, respectively, to the propulsion torque arbitration module 206. In various implementations, the hybrid optimization module 208 may be implemented in the hybrid control module 196.

The predicted and immediate torque requests received by the propulsion torque arbitration module 206 are converted from an axle torque domain (torque at the wheels) into a propulsion torque domain (torque at the crankshaft). This conversion may occur before, after, as part of, or in place of the hybrid optimization module 208.

The propulsion torque arbitration module 206 arbitrates between propulsion torque requests 290, including the converted predicted and immediate torque requests. The propulsion torque arbitration module 206 generates an arbitrated predicted torque request 261 and an arbitrated immediate torque request 262. The arbitrated torque requests 261 and 262 may be generated by selecting a winning request from among received torque requests. Alternatively or additionally, the arbitrated torque requests may be generated by modifying one of the received requests based on another one or more of the received torque requests.

For example, the propulsion torque requests 290 may include torque reductions for engine over-speed protection, torque increases for stall prevention, and torque reductions requested by the transmission control module 194 to accommodate gear shifts. The propulsion torque requests 290 may also result from clutch fuel cutoff, which reduces the engine output torque when the driver depresses the clutch pedal in a manual transmission vehicle to prevent a flare in engine speed.

The propulsion torque requests 290 may also include an engine shutoff request, which may be initiated when a critical fault is detected. For example only, critical faults may include detection of vehicle theft, a stuck starter motor, electronic throttle control problems, and unexpected torque increases. In various implementations, when an engine shutoff request is present, arbitration selects the engine shutoff request as the winning request. When the engine shutoff request is present, the propulsion torque arbitration module 206 may output zero as the arbitrated predicted and immediate torque requests 261 and 262.

In various implementations, an engine shutoff request may simply shut down the engine 102 separately from the arbitration process. The propulsion torque arbitration module 206 may still receive the engine shutoff request so that, for example, appropriate data can be fed back to other torque requestors. For example, all other torque requestors may be informed that they have lost arbitration.

The reserves/loads module 220 receives the arbitrated predicted and immediate torque requests 261 and 262. The reserves/loads module 220 may adjust the arbitrated predicted and immediate torque requests 261 and 262 to create a torque reserve and/or to compensate for one or more loads. The reserves/loads module 220 then outputs adjusted predicted and immediate torque requests 263 and 264 to the torque requesting module 224.

For example only, a catalyst light-off process or a cold start emissions reduction process may require retarded spark timing. The reserves/loads module 220 may therefore increase the adjusted predicted torque request 263 above the adjusted immediate torque request 264 to create retarded spark for the cold start emissions reduction process. In another example, the air/fuel ratio of the engine and/or the mass airflow may be directly varied, such as by diagnostic intrusive equivalence ratio testing and/or new engine purging. Before beginning these processes, a torque reserve may be created or increased to quickly offset decreases in engine output torque that result from leaning the air/fuel mixture during these processes.

The reserves/loads module 220 may also create or increase a torque reserve in anticipation of a future load, such as power steering pump operation or engagement of a heating, ventilation, and air-conditioning (HVAC) compressor clutch. The reserve for engagement of the HVAC compressor clutch may be created when the driver first requests air conditioning. The reserves/loads module 220 may increase the adjusted predicted torque request 263 while leaving the adjusted immediate torque request 264 unchanged to produce the torque reserve. Then, when the HVAC compressor clutch engages, the reserves/loads module 220 may increase the adjusted immediate torque request 264 by the estimated load of the HVAC compressor clutch.

The torque requesting module 224 receives the adjusted predicted and immediate torque requests 263 and 264. The torque requesting module 224 determines how the adjusted predicted and immediate torque requests 263 and 264 will be achieved. The torque requesting module 224 may be engine type specific. For example, the torque requesting module 224 may be implemented differently or use different control schemes for spark-ignition engines versus compression-ignition engines.

In various implementations, the torque requesting module 224 may define a boundary between modules that are common across all engine types and modules that are engine type specific. For example, engine types may include spark-ignition and compression-ignition. Modules prior to the torque requesting module 224, such as the propulsion torque arbitration module 206, may be common across engine types, while the torque requesting module 224 and subsequent modules may be engine type specific.

The torque requesting module 224 determines an air torque request 265 based on the adjusted predicted and immediate torque requests 263 and 264. The air torque request 265 may be a brake torque. Brake torque may refer to torque at the crankshaft under the current operating conditions.

Target values for airflow controlling engine actuators are determined based on the air torque request 265. More specifically, based on the air torque request 265, the air control module 228 determines a target wastegate opening area 266, a target throttle opening area 267, a target EGR opening area 268, a target intake cam phaser angle 269, and a target exhaust cam phaser angle 270. The air control module 228 determines the target wastegate opening area 266, the target throttle opening area 267, the target EGR opening area 268, the target intake cam phaser angle 269, and the target exhaust cam phaser angle 270 using model predictive control, as discussed further below.

The boost actuator module 164 controls the wastegate 162 to achieve the target wastegate opening area 266. For example, a first conversion module 272 may convert the target wastegate opening area 266 into a target duty cycle 274 to be applied to the wastegate 162, and the boost actuator module 164 may apply a signal to the wastegate 162 based on the target duty cycle 274. In various implementations, the first conversion module 272 may convert the target wastegate opening area 266 into a target wastegate position (not shown), and convert the target wastegate position into the target duty cycle 274.

The throttle actuator module 116 controls the throttle valve 112 to achieve the target throttle opening area 267. For example, a second conversion module 276 may convert the target throttle opening area 267 into a target duty cycle 278 to be applied to the throttle valve 112, and the throttle actuator module 116 may apply a signal to the throttle valve 112 based on the target duty cycle 278. In various implementations, the second conversion module 276 may convert the target throttle opening area 267 into a target throttle position (not shown), and convert the target throttle position into the target duty cycle 278.

The EGR actuator module 172 controls the EGR valve 170 to achieve the target EGR opening area 268. For example, a third conversion module 280 may convert the target EGR opening area 268 into a target duty cycle 282 to be applied to the EGR valve 170, and the EGR actuator module 172 may apply a signal to the EGR valve 170 based on the target duty cycle 282. In various implementations, the third conversion module 280 may convert the target EGR opening area 268 into a target EGR position (not shown), and convert the target EGR position into the target duty cycle 282.

The phaser actuator module 158 controls the intake cam phaser 148 to achieve the target intake cam phaser angle 269. The phaser actuator module 158 also controls the exhaust cam phaser 150 to achieve the target exhaust cam phaser angle 270. In various implementations, a fourth conversion module (not shown) may be included and may convert the target intake and exhaust cam phaser angles into target intake and exhaust duty cycles, respectively. The phaser actuator module 158 may apply the target intake and exhaust duty cycles to the intake and exhaust cam phasers 148 and 150, respectively. In various implementations, the air control module 228 may determine a target overlap factor and a target effective displacement, and the phaser actuator module 158 may control the intake and exhaust cam phasers 148 and 150 to achieve the target overlap factor and the target effective displacement.

The torque requesting module 224 may also generate a spark torque request 283, a cylinder shut-off torque request 284, and a fuel torque request 285 based on the predicted and immediate torque requests 263 and 264. The spark control module 232 may determine how much to retard the spark timing (which reduces engine output torque) from an optimum spark timing based on the spark torque request 283. For example only, a torque relationship may be inverted to solve for a target spark timing 286. For a given torque request (T_(Req)), the target spark timing (S_(T)) 286 may be determined based on: S _(T) =f ⁻¹(T _(Req),APC,I,E,AF,OT,#), where APC is an air per cylinder, I is an intake valve phasing value, E is an exhaust valve phasing value, AF is an air/fuel ratio, OT is an oil temperature, and # is a number of activated cylinders. This relationship may be embodied as an equation and/or as a lookup table. The air/fuel ratio (AF) may be the actual air/fuel ratio, as reported by the fuel control module 240.

When the spark timing is set to the optimum spark timing, the resulting torque may be as close to a minimum spark advance for maximum brake torque (MBT spark timing) as possible. Best torque refers to the maximum engine output torque that is generated for a given air flow as spark timing is advanced, while using fuel having an octane rating greater than a predetermined octane rating and using stoichiometric fueling. The spark timing at which this best occurs is referred to as an MBT spark timing. The optimum spark timing may differ slightly from MBT spark timing because of, for example, fuel quality (such as when lower octane fuel is used) and environmental factors, such as ambient humidity and temperature. The engine output torque at the optimum spark timing may therefore be less than MBT. For example only, a table of optimum spark timings corresponding to different engine operating conditions may be determined during a calibration phase of vehicle design, and the optimum value is determined from the table based on current engine operating conditions.

The cylinder shut-off torque request 284 may be used by the cylinder control module 236 to determine a target number 287 of cylinders to deactivate. In various implementations, a target number of cylinders to activate may be used. The cylinder actuator module 120 selectively activates and deactivates the valves of cylinders based on the target number 287.

The cylinder control module 236 may also instruct the fuel control module 240 to stop providing fuel for deactivated cylinders and may instruct the spark control module 232 to stop providing spark for deactivated cylinders. The spark control module 232 may stop providing spark to a cylinder once an fuel/air mixture that is already present in the cylinder has been combusted.

The fuel control module 240 may vary the amount of fuel provided to each cylinder based on the fuel torque request 285. More specifically, the fuel control module 240 may generate target fueling parameters 288 based on the fuel torque request 285. The target fueling parameters 288 may include, for example, target mass of fuel, target injection starting timing, and target number of fuel injections.

During normal operation, the fuel control module 240 may operate in an air lead mode in which the fuel control module 240 attempts to maintain a stoichiometric air/fuel ratio by controlling fueling based on air flow. For example, the fuel control module 240 may determine a target fuel mass that will yield stoichiometric combustion when combined with a present mass of air per cylinder (APC).

FIG. 3 is a functional block diagram of an example implementation of the air control module 228. Referring now to FIGS. 2 and 3, as discussed above, the air torque request 265 may be a brake torque. A torque conversion module 304 converts the air torque request 265 from brake torque into base torque. The torque request resulting from conversion into base torque will be referred to as a base air torque request 308.

Base torques may refer to torque at the crankshaft made during operation of the engine 102 on a dynamometer while the engine 102 is warm and no torque loads are imposed on the engine 102 by accessories, such as an alternator and the HVAC compressor. The torque conversion module 304 may convert the air torque request 265 into the base air torque request 308, for example, using a mapping or a function that relates brake torques to base torques. In various implementations, the torque conversion module 304 may convert the air torque request 265 into another suitable type of torque, such as an indicated torque. An indicated torque may refer to a torque at the crankshaft attributable to work produced via combustion within the cylinders.

An MPC module 312 generates the target values 266-270 to achieve the base air torque request 308 using MPC (Model Predictive Control). The MPC module 312 includes at least a state estimator module 316 and an optimization module 320.

The state estimator module 316 determines states for a control loop based on a linearized mathematical model of the engine 102, the states of the engine from a previous (e.g., last) control loop, and the target values 266-270 from the previous control loop. That is, the state estimator module 316 generates a state prediction for the engine. For example, the state estimator module 316 may determine the states for a control loop based on the relationships: x(k)=αx(k−1)+βu(k−1)+β_(v) v(k−1); and y(k)=

x(k),

where k is a k-th control loop, x(k) is a vector with entries indicative of states of the engine 102 for the k-th control loop, x(k−1) is the vector x(k) from the k−1th control loop, α is a matrix including constant values calibrated based on characteristics of the engine 102, β is a matrix including constant values calibrated based on characteristics of the engine 102, u(k−1) is a vector of including entries for the target values 266-270 used during the last control loop, y(k) is a linear combination of the vector x(k),

is a matrix including constant values calibrated based on characteristics of the engine 102, β_(v) is a matrix including constant values calibrated based on characteristics of the engine, and v is a matrix including measured disturbances. Measured disturbances modeled include parameters that impact engine behavior but cannot be directly manipulated, such as ambient pressure and/or temperature. One or more of the state parameters may be adjusted based on measured or estimated values of those parameters, collectively illustrated by feedback inputs 330. The state estimator module 316 may determine the states, for example, using a Kalman filter or another suitable type of state estimator.

The functions performed by the MPC module 312 can be generally described as follows. For k=1, . . . , N, N being in integer greater than one, do:

-   -   (1) use the above equations and the feedback inputs 330 to         obtain estimates of the states of the engine 102 at time k;     -   (2) calculate optimal values for the target values 266-270 for         the time k to minimize a cost function during the period from         the time k to a future time k+p; and     -   (3) set the target values 266-270 to the calculated optimal         values for time k+1 only. Then return to (1) for the next         control loop.         The period between times k and k+p refers to a prediction         horizon.

The cost function is the performance criterion to be minimized in the optimal control problem defined over the prediction horizon at each control loop. This function reflects the desired control goals. It may be, for example, the sum of different terms corresponding to tracking errors, for example, Σ_(i)|(u(i)−u_(ref)(i))|², for the manipulated variables to track some reference positions, μ_(i)|(y(i)−y_(ref)(i))|², for the controlled variables to track some desired setpoint values, control effort, for example, Σ_(i)|(u(i))|² or Σ_(i)|(Δu(i))|², and a penalty term for constraint violation. More generally, the cost function depends on manipulated variables u, changes in the manipulated variables from the last control loop Δu, the controlled variables y, and constraint violation penalty variable ∈. The target values 266-270 may be referred to as manipulated variables or control commands and are denoted by the variable u. Predicted parameters may be referred to as controlled variables and may be denoted by the variable y.

In a specific example, the MPC cost function is represented as a series of sums of tracking errors of the manipulated variables, reference positions, and controlled variables: V=Σ _(k=1) ^(p)Σ_(i=1) ^(ny) W _(y,i)(y _(i,k) −y _(i,k) ^(ref))²+Σ_(k=0) ^(m-1)Σ_(i=1) ^(nu) W _(u,i)(u _(k) −u _(i,k) ^(ref))²+Σ_(k=0) ^(m-1)Σ_(i=1) ^(nu) W _(Δu,i) ^(s)(Δu _(k))².

A penalty term that accounts for constraint violation and/or provides a weighted tracking error between predicted actuator positions and measured actuator positions over a prediction horizon may be represented as Σ_(i=1) ^(ny) W _(y,i)(y _(i) ^(s) −y _(i) ^(ref))², where: y ^(s) =CA ⁻¹ B+y _(n) ^(s).

That is, y^(s) is the nominal steady-state solution to the actuator system. More specifically, y^(s) is the offset by a nominal steady-state output of the actuator system, where B is a variable indicating how the one or more control inputs effect the state of the system, A is a variable showing how the previous state effects the current state, and C is a mapping from the state of the actuator system to the output command to one or more actuators in the actuator system. The use of a steady-state gain for the linearized physics-based model of the actuator system provides a means to capture the relationship between the steady-state response of the system with respect to one or more control inputs, thereby avoiding matrix multiplication over the prediction horizon. Accordingly, the cost function represents tracking errors over an infinite horizon without explicitly extending the prediction horizon, the MPC module 312 reduces tracking errors in MPC control performance without slowing down the sampling rate of the actuator system, and without generating oscillation in actuator performance in either steady-state or transient conditions. In some examples, the MPC module 312 continuously reduces tracking errors in MPC control performance utilizing the cost function as described herein. In combination with the penalty term, the full MPC cost function is therefore as follows: V=Σ _(k=1) ^(p)Σ_(i=1) ^(ny) W _(y,i)(y _(i,k) −y _(i,k) ^(ref))²+Σ_(k=0) ^(m-1)Σ_(i=1) ^(nu) W _(u,i)(u _(k) −u _(i,k) ^(ref))²+Σ_(k=0) ^(m-1)Σ_(i=1) ^(nu) W _(Δu,i) ^(s)(Δu _(k))²+Σ_(i=1) ^(ny) W _(y,i)(y _(i) ^(s) −y _(i) ^(ref))².

An actuator constraint module 360 (FIG. 2) may set actuator constraints 348 for the target values 266-270. For example, the actuator constraint module 360 may set an actuator constraint for the throttle valve 112, an actuator constraint for the EGR valve 170, an actuator constraint for the wastegate 162, an actuator constraint for the intake cam phaser 148, and an actuator constraint for the exhaust cam phaser 150.

The actuator constraints 348 for the target values 266-270 may include a maximum value for an associated target value and a minimum value for that target value. The actuator constraint module 360 may generally set the actuator constraints 348 to predetermined operational ranges for the associated actuators. More specifically, the actuator constraint module 360 may generally set the actuator constraints 348 to predetermined operational ranges for the throttle valve 112, the EGR valve 170, the wastegate 162, the intake cam phaser 148, and the exhaust cam phaser 150, respectively. However, the actuator constraint module 360 may selectively adjust one or more of the actuator constraints 348 under some circumstances.

An output constraint module 364 (FIG. 2) may set output constraints 352 for the controlled variables (y). The output constraints 352 for the controlled variables may include a maximum value for that controlled variable and a minimum value for that controlled variable. The output constraint module 364 may generally set the output constraints 352 to predetermined ranges for the associated controlled variables, respectively. However, the output constraint module 364 may vary one or more of the output constraints 352 under some circumstances.

A reference module 368 (FIG. 2) generates reference values 356 for the target values 266-270, respectively. The reference values 356 include a reference for each of the target values 266-270. In other words, the reference values 356 include a reference wastegate opening area, a reference throttle opening area, a reference EGR opening area, a reference intake cam phaser angle, and a reference exhaust cam phaser angle. The reference module 368 may determine the reference values 356, for example, based on the air torque request 265, the base air torque request 308, and/or one or more other suitable parameters.

The optimization module 320 determines the target values 266-270 using a Dantzig quadratic programming (QP) solver. A QP solver solves an optimization problem with a quadratic cost function under inequality constraints. For example, if the vector x=

^(n) represents some optimization variables, quadratic functions of x can be put into the following form: ½x ^(T) Qx−h ^(T) x+Constant, where Q is an n×n constant symmetric positive definite matrix, Constant is a constant value, and where x is the actuator position over a prediction horizon. For example, assuming an actuator system having a throttle actuator, wastegate actuator, exhaust camshaft actuator, intake camshaft actuator, and a control horizon of 3 at time k, then the vector x has size equal to 12. The throttle actuator, wastegate actuator, exhaust camshaft actuator, intake camshaft actuator at time k+1 occupy the first four components, and the same actuators occupy the next four components at future time k+2, and the same is true at future time k+3. In total, as indicated above, there are 12 components to vector x.

The optimization problem for model predictive control (MPC) has the following general form, minimize: ½x ^(T) Qx−h ^(T) x, under the linear constraints

x≤d, where h∈

^(n) h is a vector that is constant for each control loop, but can vary from control loop to control loop. Linear constraints are in the form of

x≤b, where

is a constant matrix and b is a vector that is constant for each control loop, but can vary from control loop to control loop, and x∈

^(n), Q∈

^(n×n),

∈

^(m×n), and d∈

^(m). The use of superscript T denotes transpose usage.

The optimization module 320 also includes logic for determining actuator positions when the optimization module 320 fails to solve the MPC optimization problem. When the optimization module 320 fails to solve the MPC optimization problem, the optimization module ignores the linear constraints (i.e. ignores

x≤d), and uses input constraints instead. That is, the optimization module 320 uses constraints x, where x is set to be greater than or less than a value that is specific to a given actuator. For example, if the optimization module 320 fails to determine an MPC optimized solution for a throttle actuator position, and the throttle actuator can move from 0°-90°, the optimization module 320 determines an unconstrained solution for the throttle actuator position, and then clips the unconstrained solution to the physical limits of the throttle actuator. That is, if the optimization module 320 determines the unconstrained solution for the throttle actuator position to be 120°, the solution is then clipped to the appropriate limit of the throttle actuator's physical range, i.e. 90°. Similarly, if the optimization module 320 determined the unconstrained solution for the throttle actuator position to be −15°, the unconstrained solution would be clipped to 0°. More generally, for a given control loop and a given actuator or plurality of actuators, if the optimization module 320 fails to solve the MPC optimization problem, the optimization module 320 uses the unconstrained solution clipped to the minimum or maximum constraints of the given actuator or plurality of actuators.

FIG. 4 is a flowchart depicting an example method of solving the optimization problem and determining the target values 266-270 for a single control loop. At 404, the optimization module 320 iterates from the original unconstrained solution which is already available from the simplest solution of ½x^(T) Qx−h^(T)x, namely Q⁻¹ h.

At 408, the optimization module 320 proceeds to run MPC calculations normally. At 412, the optimization module 320 determines whether MPC calculations have failed to generate a solution to the MPC optimization problem. If the solution to the MPC optimization problem has been found, no failure occurs, and the method proceeds to 416 where the solution to the MPC optimization problem is applied to the actuator system. However, if the MPC calculations have failed to generate a solution, the method proceeds to 418 where the original unconstrained solution is clipped to the input constraints. At 420, the original unconstrained solution clipped to the input constraints is applied to the actuator system. It should be noted that for each control loop the method of FIG. 4 is applied. Therefore, in some circumstances, the MPC solution may not be found for an indefinite number of control loops, while in other circumstances, the MPC solution may be found during a single control loop. While FIG. 4 is shown as ending after 420, FIG. 4 is illustrative of one control loop, and control loops may be executed at a predetermined rate.

Referring now to FIG. 5, a flowchart depicting an example method of estimating operating parameters and controlling the throttle valve 112, the intake cam phaser 148, the exhaust cam phaser 150, the wastegate 162 (and therefore the turbocharger), and the EGR valve 170 using MPC (model predictive control) is presented. Control may begin with 504 where the torque requesting module 224 determines the air torque request 265 based on the adjusted predicted and immediate torque requests 263 and 264. At 508, the torque conversion module 304 may convert the air torque request 265 into the base air torque request 308 or into another suitable type of torque for use by the MPC module 312. At 512, the state estimator module 316 determines the states of the engine 102 for the current control loop, as described above. The state estimator module 316 may determine the states, for example, using a Kalman filter.

At 516, the optimization module 320 solves the optimization problem to determine the target values 266-270, as described above. The optimization module 320 determines the target values 266-270 for the current control loop based on the target values 266-270 for the last control loop and the delta values of x*, respectively, at 520. For example only, the optimization module 320 determines the target values 266-270 by summing the delta values of x* with the target values 266-270 for the last control loop, respectively. Furthermore, if at 516 the optimization module 320 fails to find the optimal value of x*, the Linear Quadratic Regulator (LQR) solution, clipped to the input constraints for the current control loop will be sent to 520.

At 528, the first conversion module 272 converts the target wastegate opening area 266 into the target duty cycle 274 to be applied to the wastegate 162, the second conversion module 276 converts the target throttle opening area 267 into the target duty cycle 278 to be applied to the throttle valve 112. The third conversion module 280 also converts the target EGR opening area 268 into the target duty cycle 282 to be applied to the EGR valve 170 at 428. The fourth conversion module may also convert the target intake and exhaust cam phaser angles 269 and 270 into the target intake and exhaust duty cycles to be applied to the intake and exhaust cam phasers 148 and 150, respectively.

At 532, the throttle actuator module 116 controls the throttle valve 112 to achieve the target throttle opening area 267, and the phaser actuator module 158 controls the intake and exhaust cam phasers 148 and 150 to achieve the target intake and exhaust cam phaser angles 269 and 270, respectively. For example, the throttle actuator module 116 may apply a signal to the throttle valve 112 at the target duty cycle 278 to achieve the target throttle opening area 267. Also at 532, the EGR actuator module 172 controls the EGR valve 170 to achieve the target EGR opening area 268, and the boost actuator module 164 controls the wastegate 162 to achieve the target wastegate opening area 266. For example, the EGR actuator module 172 may apply a signal to the EGR valve 170 at the target duty cycle 282 to achieve the target EGR opening area 268, and the boost actuator module 164 may apply a signal to the wastegate 162 at the target duty cycle 274 to achieve the target wastegate opening area 266. While FIG. 5 is shown as ending after 532, FIG. 5 is illustrative of one control loop, and control loops may be executed at a predetermined rate.

Referring now to FIG. 6, and with continuing reference to FIGS. 1-5, an example of the system and method for penalizing steady-state tracking errors is shown. The method 600 begins at block 602 where the MPC module 312 generates a physics-based model of the actuator system. More specifically, the MPC module has a controller, a memory, and an input/output interface. The controller is a non-generalized, electronic control device having a preprogrammed digital computer or processor, a memory or non-transitory computer readable medium used to store data such as control logic, software applications, instructions, computer code and/or computer program code portions, data, lookup tables, etc., and a transceiver or input/output ports. The computer readable medium includes any type of medium capable of being accessed by a computer, such as read only memory (ROM), random access memory (RAM), a hard disk drive, a compact disc (CD), a digital video disc (DVD), or any other type of memory. A “non-transitory” computer readable medium excludes wired, wireless, optical, or other communication links that transport transitory electrical or other signals. A non-transitory computer readable medium includes media where data can be permanently stored and media where data can be stored and later overwritten, such as a rewritable optical disc or an erasable memory device. Computer code includes any type of program code, including source code, object code, and executable code. The processor is configured to execute the code or instructions. In the case of the MPC module 312 in a vehicle, the MPC module 312 may interact with and control various sub-systems in the vehicle. The MPC module 312 may include or control a dedicated Wi-Fi controller, an engine control module, a transmission control module, a body control module, an infotainment control module, etc. via the input/output ports.

The MPC module 312 further includes one or more applications or computer program code portions. The program code portions are each configured to perform a specific function or set of functions. The program code portions include software components, sets of instructions, procedures, functions, objects, classes, instances, related data, or a portion thereof adapted for implementation in a suitable compute readable program code. The program code portions may be stored within the memory or in an additional or separate memory.

In several aspects, the method 600 is carried out by the MPC module 312. The physics-based model is a linearized model of the plurality of actuators that form one of a variety of motor vehicle systems. In several examples, the actuator system may be a thermal system, a torque system, an air per cylinder (APC) system, a fuel system, a state of charge (SOC) system, a heating, ventilation, and air-conditioning (HVAC) system, an advanced driver assistance system (ADAS), or the like without departing from the scope or intent of the present disclosure. The linearized physics-based model of the actuator system is therefore a thermal model, a torque model, an APC model, a fuel model, an SOC model, an HVAC model, an ADAS model, or the like. The MPC module 312 executes a program code portion that causes the physics-based model to receive one or more inputs, including measured data from the relevant actuator system, such as a plurality of actuator system parameters or positions. For example, at block 602, the physics-based model receives system inputs 604 in the form of APC data, fuel data, state of charge data, thermal data, or the like. The MPC module 312 executes a program code portion that causes the physics-based model to utilize previous control inputs 606 from the relevant actuator system. That is, the positions of the one or more actuators of the actuator system are recorded in relation to one or more control inputs at a previous point in time. At block 608, the MPC module 312 executes a program code portion that causes the physics-based model to generate a plurality of model parameters A, B, and C. As described above in relationship to the penalty term, the first parameter A is a variable showing how the previous state of the actuator system effects the current state of the actuator system, the second parameter B is a variable indicating how a control input effects the state of the actuator system, and C is a mapping of the state of the actuator to the output command to one or more actuators in the actuator system.

At block 610, the MPC module 312 executes a program code portion that causes the physics-based model to produce a state prediction. The state prediction is generated by the state estimator module 316 and determines states for a control loop of the actuator system according to the relationships described above, namely: x(k)=αx(k−1)+βu(k−1)+β_(v) v(k−1); and y(k)=

x(k).

At block 612, an MPC solver of the MPC module 312 executes a program code portion that receives one or more measured values 614 from sensors and/or actuators disposed throughout the actuator system. In several examples, the measured values 614 may include thermal data such as measured temperatures, attitude data such as steering wheel position, throttle position, or the like, or any of a variety of other physical parameters of the motor vehicle. Furthermore, at block 612, the MPC solver executes a program code portion receives the state prediction and the model parameters (A, B, and C) from the physics-based model. The MPC solver then executes a program code portion that performs a plurality of calculations based on the data acquired from the physics-based model and the measured parameters at blocks 608, 610, and 614. Specifically, the MPC solver executes a program code portion that computes QP parameters according to the current processes being executed by the actuator system. Then the MPC solver executes a program code portion that computes a steady-state of the nonlinear system that describes the actuator system. The MPC solver executes a program code portion that calculates a steady-state gain which is then added to the QP matrices to reduce steady-state tracking errors in the MPC cost function.

The MPC module 312 then executes a program code portion that triggers the QP solver to retrieve optimal control commands 616 for each of the actuators of the actuator system. The optimal control commands 616 are shown as u₁ . . . u_(n), and represent individual commands to each of n-number of actuators in the system. The individual commands to the actuators of the actuator system may be positional commands, rate commands, or the like without departing from the scope or intent of the present disclosure. The actuator system then executes a program code portion that receives the optimal control commands 616 at block 618. At block 620, method 600 executes a program code portion that takes a measurement of the actuator system. The measurement includes the positions of each of the actuators in the actuator system, as well as a difference between the position of the actuator system and optimal positions of the actuators in the actuator system. The measurements taken at block 620 are then used as the previous control input 606 for a subsequent control loop for the actuator system.

The model predictive control system and method for penalizing steady-state tracking errors in MPC cost functions have been described above with reference to actuator systems for internal combustion propulsion systems. However, it should be appreciated that the MPC system and method may be used on or in conjunction with any of a variety of different multi-actuator systems such as: autonomous driving systems; heating, ventilation, and air conditioning systems; thermal management systems; propulsion torque control systems; state of charge systems; and the like without departing from the scope or intent of the present disclosure.

A model predictive control system and method for increasing computational efficiency of the present disclosure offers several advantages. These include: improved engine response, reduced computational time between an engine torque request and an engine torque response, decreased driveline lash, improved noise, vibration, and harshness (NVH) characteristics, as well as computational redundancy.

The foregoing description is merely illustrative in nature and is in no way intended to limit the disclosure, its application, or uses. The broad teachings of the disclosure can be implemented in a variety of forms. Therefore, while this disclosure includes particular examples, the true scope of the disclosure should not be so limited since other modifications will become apparent upon a study of the drawings, the specification, and the following claims. As used herein, the phrase at least one of A, B, and C should be construed to mean a logical (A OR B OR C), using a non-exclusive logical OR, and should not be construed to mean “at least one of A, at least one of B, and at least one of C.” It should be understood that one or more steps within a method may be executed in different order (or concurrently) without altering the principles of the present disclosure.

In this application, including the definitions below, the term “module” or the term “controller” may be replaced with the term “circuit.” The term “module” may refer to, be part of, or include: an Application Specific Integrated Circuit (ASIC); a digital, analog, or mixed analog/digital discrete circuit; a digital, analog, or mixed analog/digital integrated circuit; a combinational logic circuit; a field programmable gate array (FPGA); a processor circuit (shared, dedicated, or group) that executes code; a memory circuit (shared, dedicated, or group) that stores code executed by the processor circuit; other suitable hardware components that provide the described functionality; or a combination of some or all of the above, such as in a system-on-chip.

The module may include one or more interface circuits. In some examples, the interface circuits may include wired or wireless interfaces that are connected to a local area network (LAN), the Internet, a wide area network (WAN), or combinations thereof. The functionality of any given module of the present disclosure may be distributed among multiple modules that are connected via interface circuits. For example, multiple modules may allow load balancing. In a further example, a server (also known as remote, or cloud) module may accomplish some functionality on behalf of a client module.

The term code, as used above, may include software, firmware, and/or microcode, and may refer to programs, routines, functions, classes, data structures, and/or objects. The term shared processor circuit encompasses a single processor circuit that executes some or all code from multiple modules. The term group processor circuit encompasses a processor circuit that, in combination with additional processor circuits, executes some or all code from one or more modules. References to multiple processor circuits encompass multiple processor circuits on discrete dies, multiple processor circuits on a single die, multiple cores of a single processor circuit, multiple threads of a single processor circuit, or a combination of the above. The term shared memory circuit encompasses a single memory circuit that stores some or all code from multiple modules. The term group memory circuit encompasses a memory circuit that, in combination with additional memories, stores some or all code from one or more modules.

The term memory circuit is a subset of the term computer-readable medium. The term computer-readable medium, as used herein, does not encompass transitory electrical or electromagnetic signals propagating through a medium (such as on a carrier wave); the term computer-readable medium may therefore be considered tangible and non-transitory. Non-limiting examples of a non-transitory, tangible computer-readable medium are nonvolatile memory circuits (such as a flash memory circuit, an erasable programmable read-only memory circuit, or a mask read-only memory circuit), volatile memory circuits (such as a static random access memory circuit or a dynamic random access memory circuit), magnetic storage media (such as an analog or digital magnetic tape or a hard disk drive), and optical storage media (such as a CD, a DVD, or a Blu-ray Disc).

The apparatuses and methods described in this application may be partially or fully implemented by a special purpose computer created by configuring a general purpose computer to execute one or more particular functions embodied in computer programs. The functional blocks, flowchart components, and other elements described above serve as software specifications, which can be translated into the computer programs by the routine work of a skilled technician or programmer.

The computer programs include processor-executable instructions that are stored on at least one non-transitory, tangible computer-readable medium. The computer programs may also include or rely on stored data. The computer programs may encompass a basic input/output system (BIOS) that interacts with hardware of the special purpose computer, device drivers that interact with particular devices of the special purpose computer, one or more operating systems, user applications, background services, background applications, etc.

The computer programs may include: (i) descriptive text to be parsed, such as HTML (hypertext markup language) or XML (extensible markup language), (ii) assembly code, (iii) object code generated from source code by a compiler, (iv) source code for execution by an interpreter, (v) source code for compilation and execution by a just-in-time compiler, etc. As examples only, source code may be written using syntax from languages including C, C++, C#, Objective C, Haskell, Go, SQL, R, Lisp, Java®, Fortran, Pert, Pascal, Curl, OCaml, Javascript®, HTML5, Ada, ASP (active server pages), PHP, Scala, Eiffel, Smalltalk, Erlang, Ruby, Flash®, Visual Basic®, Lua, and Python®.

None of the elements recited in the claims are intended to be a means-plus-function element within the meaning of 35 U.S.C. § 112(f) unless an element is expressly recited using the phrase “means for,” or in the case of a method claim using the phrases “operation for” or “step for.” 

What is claimed is:
 1. A method for controlling an actuator system of a motor vehicle, the method comprising: utilizing a model predictive control (MPC) module with an MPC solver to determine optimal positions of one or more actuators of the actuator system; receiving a plurality of actuator system parameters; triggering the MPC solver to generate one or more control commands from the plurality of actuator system parameters; computing a steady-state solution of the actuator system over a prediction horizon; generating steady-state predictions of positions of the one or more actuators of the actuator system based on actuator system inputs, one or more environmental conditions, and a linearized physics-based model of the actuator system; and applying a cost function to reduce a steady-state tracking error in the one or more control commands from the MPC solver; and applying the one or more control commands to alter positions of the one or more actuators, and applying a penalty term to the steady-state predictions of positions of the one or more actuators to limit a difference between a steady-state prediction of the actuator system and a solution from the MPC solver, wherein the penalty term has the following equation: $\sum\limits_{i = 1}^{ny}{W_{y,i}\left( {y_{i}^{s} - y_{i}^{ref}} \right)}^{2}$ where y^(s)=CA⁻¹B+y_(n) ^(s), such that y^(s) is a nominal steady-state solution to the actuator system, W_(y,i) is a predetermined calibrated weight, B indicates the effects of one or more control inputs on a state of the actuator system, A expresses effects of a previous state on a current state, and C maps the current state of the actuator system to one or more output positions of the one or more actuators in the actuator system.
 2. The method of claim 1 wherein triggering the MPC solver further comprises: capturing a relationship between a steady-state response of the actuator system and one or more control inputs; and calculating a steady-state gain for the actuator system.
 3. The method of claim 2 wherein calculating a steady-state gain for the actuator system further comprises: mapping states of the one or more actuators to output positions of the one or more actuators; determining a relationship between a previous state of the one or more actuators and a current state of the one or more actuators; and determining a relationship between the one or more control inputs and the current state of the one or more actuators.
 4. The method of claim 1 wherein computing a steady-state solution of the actuator system further comprises: determining a steady-state non-linearized solution of the actuator system based on a nominal input.
 5. The method of claim 1 wherein receiving a plurality of actuator system parameters further comprises: receiving one or more control inputs to the actuator system; measuring one or more environmental conditions; calculating a linearized physics-based model of the actuator system; and determining one or more actuator system inputs to the linearized physics-based model.
 6. The method of claim 5 further comprising: generating one or more physical parameters from the linearized physics-based model.
 7. The method of claim 1 wherein applying a cost function further comprises: calculating the predetermined calibrated weight for each control command over the prediction horizon, wherein the prediction horizon is an infinite horizon.
 8. The method of claim 7 wherein applying the one or more control commands to alter positions of the one or more actuators further comprises: taking a measurement of the actuator system once the one or more control commands have been applied to the one or more actuators; and applying the measurement of the actuator system to the linearized physics-based model.
 9. The method of claim 8 wherein applying the measurement further comprises: applying the measurement of the actuator system as a previous control input to the linearized physics-based model of the actuator system.
 10. The method of claim 1 wherein controlling an actuator system further comprises: controlling one or more of an air per cylinder (APC) system; a fuel system; a state of charge system; a heating, ventilation, and air conditioning system; and an advanced driver assistance system (ADAS).
 11. A system for controlling an actuator system of a motor vehicle, the system comprising: one or more of an air per cylinder (APC) system; a fuel system; a state of charge system; a heating, ventilation, and air conditioning system; and an advanced driver assistance system (ADAS); one or more actuators; a model predictive control (MPC) module with an MPC solver that determines optimal positions of the one or more actuators of the actuator system, the MPC module having a controller, a memory, and an input/output interface, the memory storing program code portions, and the controller configured to execute the program code portions, the program code portions comprising: a program code portion that receives a plurality of actuator system parameters; a program code portion that triggers the MPC solver to generate one or more control commands from plurality of actuator system parameters; a program code portion that computes a steady-state solution of the actuator system over a prediction horizon; a program code portion that generates steady-state predictions of positions of the one or more actuators of the actuator system based on the actuator system inputs, one or more environmental conditions, and a linearized physics-based model of the actuator system; a program code portion that applies a cost function to reduce a steady-state tracking error in the one or more control commands from the MPC solver; a program code portion that applies the one or more control commands via the input/output interface to alter positions of the one or more actuators; and a program code portion that applies a penalty term to the steady-state predictions of positions of the one or more actuators to limit a difference between a steady-state prediction of the actuator system and a solution from the MPC solver, wherein the penalty term has the following equation: $\sum\limits_{i = 1}^{ny}{W_{y,i}\left( {y_{i}^{s} - y_{i}^{ref}} \right)}^{2}$ where y^(s)=CA⁻¹B+y_(n) ^(s), such that y^(s) is a nominal steady-state solution to the actuator system, W_(y,i) is a predetermined calibrated weight, B indicates the effects of one or more control inputs on a state of the system, A expresses effects of a previous state on a current state, and C maps a current state of the actuator system to one or more output positions of one or more actuators in the actuator system.
 12. The system of claim 11 wherein the program code portion that triggers the MPC solver further comprises: a program code portion that captures a relationship between a steady-state response of the actuator system and one or more control inputs; and a program code portion that calculates a steady-state gain for the actuator system.
 13. The system of claim 12 wherein the program code portion that calculates a steady-state gain for the actuator system further comprises: a program code portion that maps states of the one or more actuators to output positions of the one or more actuators; a program code portion that determines a relationship between a previous state of the one or more actuators and a current state of the one or more actuators; and a program code portion that determines a relationship between the one or more control inputs and the current state of the one or more actuators.
 14. The system of claim 11 wherein the program code portion that computes a steady-state solution of the actuator system further comprises: a program code portion that determines a steady-state non-linearized solution of the actuator system based on a nominal input.
 15. The system of claim 11 wherein the program code that receives a plurality of actuator system parameters further comprises: a program code portion that receives one or more control inputs to the actuator system; a program code portion that measures one or more environmental conditions; a program code portion that calculates a linearized physics-based model of the actuator system; and a program code portion that determines one or more actuator system inputs to a linearized physics-based model.
 16. The system of claim 15 further comprising: a program code portion that generates one or more physical parameters from the linearized physics-based model.
 17. The system of claim 11 wherein the program code portion that applies a cost function further comprises: a program code portion that calculates the predetermined calibrated weight for each control command over the prediction horizon, wherein the prediction horizon is an infinite horizon.
 18. The system of claim 17 wherein the program code portion that applies the one or more control commands to alter positions of the one or more actuators further comprises: a program code portion that takes a measurement of the actuator system once the one or more control commands have been applied to the one or more actuators; and a program code portion that applies the measurement of the actuator system to the linearized physics-based model.
 19. The system of claim 18 wherein the program code portion that applies the measurement further comprises: a program code portion that applies the measurement of the actuator system as a previous control input to the linearized physics-based model of the actuator system.
 20. A method for controlling an actuator system of a motor vehicle, the method comprising: utilizing a model predictive control (MPC) module with an MPC solver to determine optimal positions of one or more actuators of the actuator system; receiving a plurality of actuator system parameters including: receiving one or more control inputs to the actuator system; measuring one or more environmental conditions; calculating a linearized physics-based model of the actuator system; and determining one or more actuator system inputs to the linearized physics-based model; triggering the MPC solver to generate one or more control commands from plurality of actuator system parameters by: capturing a relationship between a steady-state response of the actuator system and the one or more control inputs; computing a steady-state non-linearized solution of the actuator system over an infinite prediction horizon based on a nominal input; and calculating a steady-state gain for the actuator system by: mapping states of the one or more actuators to output positions of the one or more actuators; determining a relationship between a previous state of the one or more actuators and a current state of the one or more actuators; and determining a relationship between the one or more control inputs and the current state of the one or more actuators; generating a steady-state prediction of the positions of the one or more actuators of the actuator system based on actuator system inputs, one or more environmental conditions, and the linearized physics-based model of the actuator system; generating one or more physical parameters from the linearized physics-based model; applying a cost function to reduce a steady-state tracking error in the one or more control commands from the MPC solver, wherein the cost function is calculated by applying a calibrated weight to the steady-state prediction to limit a difference between the steady-state prediction and a solution from the MPC solver; and wherein the calibrated weight is calculated for each control command over the infinite prediction horizon; applying the one or more control commands to alter positions of the one or more actuators, comprising taking a measurement of the actuator system once the one or more control commands have been applied to the one or more actuators; applying the measurement of the actuator system to the linearized physics-based model by applying the measurement of the actuator system as a previous control input to the linearized physics-based model of the actuator system; and applying a penalty term to the steady-state predictions of positions of the one or more actuators to limit a difference between a steady-state prediction of the actuator system and a solution from the MPC solver, wherein the penalty term has the following equation: $\sum\limits_{i = 1}^{ny}{W_{y,i}\left( {y_{i}^{s} - y_{i}^{ref}} \right)}^{2}$ where y^(s)=CA⁻¹B+y_(n) ^(s), such that y^(s) is a nominal steady-state solution to the actuator system, W_(y,i) is a predetermined calibrated weight, B indicates the effects of one or more control inputs on a state of the actuator system, A expresses effects of the previous state on the current state, and C maps a current state of the actuator system to one or more output positions of one or more actuators in the actuator system. 